Differential Shannon Entropies and Mutual Information in a Curve Crossing System: Adiabatic and Diabatic Decompositions

The differential Shannon entropy provides a measure for the localization of a wave function. We regard the vibrational wave packet motion in a curve crossing system and calculate time-dependent entropies. Using a numerical example, we analyze how localization inside diabatic and adiabatic states can be accessed and discuss the differences between these two representations. In order to do so, we extend the usual entropy definition and introduce novel state-selective entropies. These quantities contain information on the form of the nuclear density components on the one hand and on the state population on the other, and it is shown how the contribution of the population can be removed. Having the state-selective entropies at hand, two additional functions derived from these, namely, the conditional entropy and the mutual information, are determined and compared. We find that these quantities relate closely to correlation effects rooted in different electronic properties of the system.